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A particle is projected under gravity with a speed $v_0$. Using $\text{W-E}$ theorem, find the speed of the particle as the function of vertical distance $y$.

A stone is tied to a rope of length $2$ m and is whirled above his head horizontally by a man at a height of $9\text{m}$ from the ground. The stone covers a horizontal distance of $20\text{m}$ when the rope breaks. What is the magnitude of the centripetal acceleration when the stone was in the circular motion?

Two metal spheres (radii $r_1,r_2$ with $r_1<r_2$) are very far apart but are connected by a thin wire. If their combined charge is $Q$, then what is their common Potential?

The relation between speed of sound in moist air $v_m$ and dry air $v_d$ at the same temperature and pressure will be

At what angle with the horizontal should a ball be thrown so that the range $R$ is related to the time of flight $\left(T\right)$ as $R=5T^2?(\text{Take g}=10{\text{m/s}}^2)$

A particle of mass m is projected with velocity v making an angle of ${45}^{\circ }$ with the horizontal. Themagnitude of the angular momentum of the particle about the point of projection when the particle is at its maximum height is (where g = acceleration due to gravity)

At a height of $0.4m$ from the ground, the velocity of a projectile in vector form is$\overrightarrow{v}=(6\hat{i}+2\hat{j})m/s.$ The angle of projection is

$(g=10m/s^2)$

Figure shows a capillary tube of radius $r$ dipped into water. The atmospheric pressure is $P_0$ and the capillary rise of water is $h$. $s$ is the surface tension for water-glass.





The pressure inside water at the point $A$ (lowest point of the meniscus) is

5 litre of benzene weighs

The equation of a progressive wave is $y=0.03\sin 2\pi [\frac{t}{0.01}-\frac{x}{0.30}]$ here $x$ and $y$ are in metres and $t$ is in seconds. The velocity of propagation of the wave is

Find the total torque acting on the body shown in the figure about the point $O$

The springs shown in the figure are all unstretched in the beginning when a man starts pulling the block. The man exerts a constant force F on the block. Find the amplitude and the frequency of the motion of the block.

A sphere of radius $R$ is half submerged in liquid of density $\rho$. If the sphere is slightly pushed down and released, it oscillates, then what is the frequency of its oscillation ?

If a body moving in a circular path maintains constant speed of $10\text{m/s}$, then which of the following graphs correctly describes the relation between acceleration and radius?

A particle executes S.H.M (a) What fraction of total energy is kinetic? What fraction is potential when displacement is one half of the amplitude?

A man is $25\text{m}$ behind a bus, when the bus starts accelerating at $2{\text{m/s}}^2$ and man starts moving with constant velocity of $10\text{m/s}$. Time taken by him to board the bus is

Block $A$ is placed on block $B$, whose mass is greater than that of $A$. There is friction between the blocks, while the ground is smooth. A horizontal force $P$, increasing linearly with time, begins to act on $A$. The accelerations $a_1$ and $a_2$ of $A$ and $B$ respectively are plotted against time ($t$). Choose the correct graph.

The table gives the initial length $l_0$, change in temperature $\Delta T$ and change in length $\Delta l$ of four rods. Which rod has greatest coefficient of linear expansion

$\begin{array}{cccc}\text{Rod}& l_0\left(m\right)& \Delta T{(}^{\circ }C& \Delta l\left(m\right)\\ A_1& 1& 100& 1\\ A_2& 1& 100& 2\\ A_3& 1.5& 50& 3\\ A_4& 2.5& 20& 4\end{array}$

The equation of the line making ${53}^{\circ }$ with positive $x-axis$ and passing through $(2,4)$ is

[Hint:- $\tan {53}^{\circ }=\frac{4}{3}$]

Small amplitude progressive wave in a stretched string has a speed of 100 cm/s, and frequency 100 Hz. The phase difference between two points 2.75 cm apart on the string in radians, is

The magnitude of vector $\overrightarrow{A},\overrightarrow{B}$ and $\overrightarrow{C}$ are respectively 12, 5 and 13 units and $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}$ then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is

Block A is heavier than Block B, and when they are put on a wedge connected through a pulley, they start sliding. Identify the direction of friction on both the blocks.

In an experiment, we measure quantities $a,b$ and $c$; then $x$ is calculated from the formula $x=\frac{a{b}^2}{c^3}$ . The percentage errors in $a,b$ and $c$ are $\pm 1\%$, $\pm 3\%$ and $\pm 2\%$ respectively. The percentage error in $x$ can be

A particle is projected with a certain velocity at an angle $\alpha$ above the horizontal from the foot of an inclined plane of inclination ${30}^{\circ }$. If the particle strikes the plane normally. then $\alpha$ is equal to

Potentiometer wire is $100\text{cm}$ long and a constant potential difference is maintaned across it. Two cells are connected in series first to support one another and then in opposite direction. The balance points are obtained at $50\text{cm}$ and $10\text{cm}$ from the positive end of the wire in the two cases. The ratio of emf's is:

The equation of particle executing simple harmonic motion $x=10\text{sin}(\pi t+\frac{\pi }{6})$ where $x,t$ are in SI units. Find the velocity of the particle at $t=1$ seconds.

A coil of resistance $20\Omega$ and inductance $5H$ has been connected to a $100V$ battery The energy stored in the coil after a long time is

The truth table for system of four NAND gates as shown in the figure is

Rain is falling downwards with a velocity of $3\text{km/h}$. A man walks in the rain with a velocity of $4\text{km/h}$. Raindrops will appear to be falling on the man with a velocity of

In the arrangement shown in the figure, coefficient of friction between the two blocks is, $\mu =0.5$. The force of friction acting between the two blocks is

Evaluate $\int x{e}^{x}dx$

Due to capillary action, a liquid will rise in a tube, if the angle of contact is

Escape velocity from earth is about $11km{s}^{-1}$. Escape velocity from a planet having twice the radius and same mean density as the earth is.

Immediately on cutting the taut string, the acceleration of one of the blocks is found to be $2m{s}^{-2}.$ If $m_1=6kg,m_2$ is equal to $(g=10m{s}^{-2})$

If each capacitor has capacitance $C$ in the figure $\left(a\right)$ then find $C_{AB}$.

Three rods each of mass $m$ and length $L$ are joined to form an equilateral triangle as shown in the figure. What is the moment of inertia about an axis passing through the centre of mass of the system and perpendicular to the plane?

Which of the following component of EM wave spectrum is the least energetic:

A sphere, a cube and a thin circular plate have the same mass and are made of the same material. All of them are heated to the same temperature. The rate of cooling is

A traveling wave in a stretched string is described by the equation;

y = A sin (kx- $\omega$t). The maximum particle velocity is :

In helium nucleus, there are

The ionisation energy of 10 times ionised sodium atom (given the ionisation energy of H atom is 13.6eV) is

What would happen if we touched the metal sphere on the side closer to the Van de Graaff generator?

The variation of velocity of a particle moving along a straight line is shown in the figure. The magnitude of displacement of the particle in $8\text{s}$ is:

A projectile thrown with velocity $v$ making angle ${30}^{\circ }$ with vertical gains maximum height $100m$ in the time for which the projectile remains in air, the time of flight of the projectile in seconds is (take $g=10{m/s}^2$)

If $y=e^x.\cot x$ then $dy/dx$ will be